Kalman Particle Filtering of Point Processes Observation

Kalman Filtering for Manufacturing Processes

Kalman filtering for self-similar processes

In our earlier work, we introduced a class of stochastic processes obeying a structure of the form, E [ X ( t ) X ( t X ) ] = R(X), t , X > 0, and outlined a mathematical framework for the modeling and analysis for these processes. We referred to this class of processes as scale stationary processes. We demonstrated that scale stationarity framework leads to engineering oriented mathematical to...

Non-regular processes and singular Kalman filtering

Contrary to the continuous-time case, a discrete-time process y can be represented by minimal linear models (see (1.1) below), which may either have a non-singular or a singular D matrix. In fact, models with D = 0 have been commonly used in the statistical literature. On the other hand, for models with a singular D matrix the Riccati difference equation of Kalman filtering involves in general ...

Analysis of video-based microscopic particle trajectories using Kalman filtering.

The fidelity of the trajectories obtained from video-based particle tracking determines the success of a variety of biophysical techniques, including in situ single cell particle tracking and in vitro motility assays. However, the image acquisition process is complicated by system noise, which causes positioning error in the trajectories derived from image analysis. Here, we explore the possibi...

Particle filtering with pairwise Markov processes

The estimation of an unobservable process x from an observed process y is often performed in the framework of Hidden Markov Models (HMM). In the linear Gaussian case, the classical recursive solution is given by the Kalman filter. On the other hand, particle filters are Monte Carlo based methods which provide approximate solutions in more complex situations. In this paper, we consider Pairwise ...